Creating lists of Pairs etc. per basis atom would be enough for this. Then, the corresponding loops could also be parallelized over atoms in the basis cell.
For custom systems, where a large basis cell is used, e.g. to accomodate spatial distribution of interactions, this would make a big performance difference.

Note: currently there is one list of Pairs for the "first" basis cell. This list cannot be run over in parallel, as one spin may appear multiple times, creating race conditions.